aiqbench analysis
This research addresses the practical challenge of unknown GP priors in blackbox optimization by introducing two Thompson Sampling-based algorithms that jointly select priors and minimize regret. Theoretical analysis confirms sublinear regret bounds for the proposed HyperPrior method, while experiments validate its superiority over standard maximum likelihood estimation approaches. These advances offer a more robust framework for practitioners relying on Gaussian process bandits where prior assumptions cannot be guaranteed.
Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling
arXiv:2502.01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we study two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) that disqualifies priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS) that utilizes a bi-level Thompson sampling scheme. We theoretically analyze the algorithms and establish a sublinear regret bound for HP-GP-TS. In addition, we demonstrate the effectiveness of these algorithms compared to the alternatives through extensive experiments with synthetic and real-world data.
Abstract:Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions. The characteristics of the unknown function depend heavily on the assumed GP prior. Most work in the literature assume that this prior is known but in practice this seldom holds. Instead, practitioners often rely on maximum likelihood estimation to select the hyperparameters of the prior - which lacks theoretical guarantees. In this work, we study two algorithms for joint prior selection and regret minimization in GP bandits based on GP Thompson sampling (GP-TS): Prior-Elimination GP-TS (PE-GP-TS) that disqualifies priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS) that utilizes a bi-level Thompson sampling scheme. We theoretically analyze the algorithms and establish a sublinear regret bound for HP-GP-TS. In addition, we demonstrate the effectiveness of these algorithms compared to the alternatives through extensive experiments with synthetic and real-world data.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2502.01226 [cs.LG]
(or arXiv:2502.01226v4 [cs.LG] for this version)
Full text under the publisher's open licence · 157 words
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